Heat the butter and oil in a large heavy pan. Add the onions, and cook slowly until soft and brown, about 45 minutes. Add vinegar and honey, tossing to coat. Set aside.

Carmelized onion goodness!

Combine the squash and stock in a large pot. Simmer until squash is soft if you are using fresh. Turn off the heat, add the milk, and blend with an immersion blender until smooth. Salt and pepper to taste; I used about 1 tsp. salt and 1 tsp. pepper.

Basically a squash soup...

Slice all of the cheeses. Combine the ricotta, eggs and sage in a bowl. Add 1/2 tsp. salt and 1/2 tsp. pepper.

A cheese melange!

Begin to layer your lasagna: sauce (squash), pasta, 1/3 of the cheeses including ricotta, 1/2 of the onion, repeat once. Finish with a layer of sauce, pasta, remainder of sauce, and the remainder of cheese. This will seem rather soupy, but the no-cook noodles absorb a fair amount of liquid.

The finished assembly

Cook covered for 25 minutes, and finish cooking uncovered for another 35 minutes, or until hot and bubbly.